Find the value of b. Then find the angle measures of the pentagon.

b = 90

Step-by-step explanation:

Sum the interior angles of the pentagon and equate to 540

Starting from the top and going clockwise

b + b + 45 + 90 + 2b - 90 + b = 540 ← simplify left side

b + 45 = 540 ( multiply through by 2 to clear the fraction )

11b + 90 = 1080 ( subtract 90 from both sides )

11b = 990 ( divide both sides by 11 )

b = 90

Thus

b + 45 = 90 + 45 = 135

2b - 90 = 2(90) - 90 = 180 - 90 = 90

b = × 90 = 135

The angle measure from the top clockwise are

90°, 135°, 90°, 90°, 135°

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.